Multiscale modeling of θ′ precipitation in Al–Cu binary alloys

We present a multiscale model for studying the growth and coarsening of θ′ precipitates in Al–Cu alloys. Our approach utilizes a novel combination of the mesoscale phase-field method with atomistic approaches such as first-principles total energy and linear response calculations, as well as a mixed-space cluster expansion coupled with Monte Carlo simulations. We give quantitative first-principles predictions of: (i) bulk energetics of the Al–Cu solid solution and θ′ precipitate phases, (ii) interfacial energies of the coherent and semi-coherent θ′/Al interfaces, and (iii) stress-free misfit strains and coherency strain energies of the θ′/Al system. These first-principles data comprise all the necessary energetic information to construct our phase-field model of microstructural evolution. Using our multiscale approach, we elucidate the effects of various energetic contributions on the equilibrium shape of θ′ precipitates, finding that both the elastic energy and interfacial energy anisotropy contributions play critical roles in determining the aspect ratio of θ′ precipitates. Additionally, we have performed a quantitative study of the morphology of two-dimensional multi-precipitate microstructures during growth and coarsening, and compared the calculated results with experimentally observed morphologies. Our multiscale first-principles/phase-field method is completely general and should therefore be applicable to a wide variety of problems in microstructural evolution.